As machine learning algorithms continue to enable and accelerate physics calculations, the development of problem-specific physics-informed machine learning approaches is becoming more sophisticated, impactful, and important. I will describe recent advances in generative modelling emerging from the challenge of exact sampling from known probability distributions in the context of lattice quantum field theory calculations in particle and nuclear physics. I will discuss in particular flow-based generative models, outline the importance of guarantees of exactness and the incorporation of complex symmetries (e.g., gauge symmetry) into model architectures, and show how this can be achieved.